This invention relates to an apparatus and a method for shaping an optical surface. More particularly, the invention relates to an apparatus and a method for generating a deterministic polishing process for an optical surface.
Optical elements, such as lenses and mirrors, in an optical system provide for the shaping of radiation fronts, such as light fronts. Shaping of radiation fronts includes focusing, collimating, dispersing, amplifying, and the like. The shapes of the surfaces of optical elements (sometimes referred to as workpieces) are one feature of the optical elements that contribute to shaping radiation fronts as desired. The forming of optical surfaces of optical elements typically includes a series of basic process steps including: i) shaping, ii) grinding, iii) full-aperture polishing, and sometimes iv) sub-aperture polishing. With significant innovation and development over the years in i) shaping and iv) sub-aperture polishing, both shaping and sub-aperture polishing have become relatively deterministic. For example, with the advent of both computer numerical controlled (CNC) grinding machines and sub-aperture polishing tools, such as magnetorheological finishing (MRF), shaping and sub-aperture polishing have become more deterministic. That is, these processes may be applied to an optical element, and the resultant surface of the optical element will have a shape that is desired without significant human monitoring of the process. For example, a workpiece (e.g., a fused silica blank) might be placed in a CNC machine for shaping, and the CNC machine might shape the blank without the need for a human to stop the CNC machine to change any of the control parameters of the CNC machine.
However, the intermediate stages: ii) full aperture grinding and iii) full aperture polishing are relatively less deterministic processes. That is, various grinding techniques and polishing techniques may be applied to an optical element, but to achieve a desired surface shape, the attention, insight, and intuition of an optician are typically required. Specifically, grinding techniques and polishing techniques are often applied to a surface iteratively because measurements of the surface are made as an optician monitors the applied techniques and makes adjustments to the techniques. Without the optician's monitoring and talents, the surfaces of optical elements during grinding and polishing are highly likely to have a shape that is not desired. That is, the resultant optical elements might not be useful for their intended purposes, such as shaping radiation fronts as desired, or the optical elements might be damaged (e.g., in high energy applications) during use due to less than optimal surface shape.
The ability to deterministically finish a surface during full aperture grinding and full aperture polishing provides for obtaining a desired surface shape of an optical element in a manner that is relatively more repeatable, less intermittent, and relatively more economically feasible than traditional grinding and polishing techniques. The development of a scientific understanding of the material removal rate from a surface is an important step in transitioning to deterministic grinding and polishing.
At the molecular level, material removal during glass polishing is dominated by chemical processes. The most common polishing media for silica glass is cerium oxide. Cerium oxide polishing can be described using the following basic reaction:═Ce—OH+HO—Si≡→═Ce—O—Si≡+H2OThe surface of the cerium oxide particle is cerium hydroxide, which condenses with the glass surface (silanol surface) to form a Ce—O—Si bond. The bond strength of this new oxide is greater than the bond strength of the Si—O—Si bond (i.e., the glass). Hence, polishing is thought to occur as ceria particles repeatedly tear away individual silica molecules. It is well known that properties such as pH, isoelectric point, water interactions, slurry concentration, slurry particle size distribution, and other chemical properties can influence the removal rate of material from a surface.
At the macroscopic level, material removal (e.g., of thickness h) from a surface has been historically described by the widely used Preston's equation:
            ⅆ      h              ⅆ      t        =            k      p        ⁢          σ      o        ⁢          V      r      where
      ⅆ    h        ⅆ    t  is the average thickness removal rate, σo is the applied pressure of a lap on a workpiece, and Vr is the average relative velocity of the polishing particle relative to the workpiece. The molecular level effects are described macroscopically by the Preston's constant (kp). The molecular level effects include the effects of the particular slurry used for polishing. As can be seen from Preston's equation, the rate of removal of material from a surface of a workpiece increases linearly with pressure σo and velocity Vr. Many studies, particularly those in the chemical mechanical polishing (CMP) literature for silicon wafer polishing, have expanded Preston's model to account for slurry fluid flow and hydrodynamic effects, Hertzian contact mechanics, influence of asperity microcontact, lap bending, and the mechanics of contact on the pressure distribution. Only a few of these studies focus on understanding and predicting surface shape (or global non-uniformity).
None of the these studies has described the general case involving the interplay of the multiple effects such that the material removal and the final surface shape of the workpiece can be quantitatively determined. Therefore, new apparati and methods are needed to measure and predict material removal and surface shape for a workpiece (such as a silica glass workpiece) that has been polished using polishing slurry (such as a cerium oxide slurry) on a lap (such as a polyurethane lap) under a systematic set of polishing conditions. Further, a spatial-and-temporal-polishing apparatus and a spatial-and-temporal-polishing method are needed to simulate the experimental data incorporating: 1) the friction coefficient as function of velocity (Stribeck friction curve), 2) the relative velocity, which is determined by the kinematics of the lap and the workpiece motions, and 3) the pressure distribution, which is shown to be dominated by: a) moment forces, b) lap viscoelasticity, and c) workpiece-lap mismatch.